The present invention relates to apparatus and methods for determining the polarization of electromagnetic signals.
Electromagnetic signals such as radio waves and light have a property referred to as polarization. Radar operates by transmitting an electromagnetic signal to a target and comparing the signal reflected from the target with the transmitted signal. In modern electronic warfare, targets avoid detection from enemy radar by using various countermeasures such as, jamming an enemy radar signal impinging on the target with a signal denying range information to the enemy and creating false reflected signals to deceive the enemy radar system. To be effective, the signals created by the countermeasure system should have characteristics such as polarization corresponding to the signal characteristics expected by the enemy system as, for example, characteristics of the return signals expected by an enemy radar system. In some cases, the enemy radar may change its signal polarization rapidly. Such a radar system is referred to as a xe2x80x9cpolarization agile.xe2x80x9d If the enemy radar is polarization agile, the countermeasure system must be capable of determining the polarization of the transmitted signal rapidly, so that the countermeasure system can change the signals which it emits. For example, a jamming system carried on an aircraft and intended to defeat a polarization agile enemy radar system should determine the polarization of the incoming radar signal and alter the polarization of the jamming signal accordingly. If the jamming system does not do this, the jamming signal will not match the polarization of the return signals from the aircraft. The enemy radar receiver can reject the jamming signals and acquire meaningful return signals. Delay in measuring the incoming signal polarization can allow the enemy system to acquire meaningful return signals for a sufficient time to find the position of the aircraft. Conversely, where a radar or communications system must overcome enemy jamming, it is desirable to measure the polarization of the jamming signal and transmit the radar or communications signal with a different polarization.
However, traditional polarization measuring techniques do not provide polarization measurements rapidly enough to counteract a polarization agile enemy system. Just as the receiving system becomes accustomed to one polarization, the enemy system changes polarization.
At a given point in space along the path of an electromagnetic wave and at a given instant in time, an electric field points in a particular direction, denoted by a vector, {right arrow over (E)}. This vector is perpendicular to the direction of travel of the signal or xe2x80x9cpropagation vector.xe2x80x9d The polarization of an electromagnetic wave is described by the orientation of the electric field vector and the manner in which this vector varies with time.
The polarization vector can be split into components Ex and Ey along orthogonal x and y axes perpendicular to the direction of travel of the electromagnetic wave. The component along the x axis commonly is referred to as the xe2x80x9chorizontalxe2x80x9d component, whereas the component along the y axis is referred to as the xe2x80x9cverticalxe2x80x9d component. Although these terms are used herein, it should be appreciated that these directions may be arbitrary directions unrelated to the normal gravitational frame of reference. At any given point in space, Ex and Ey vary with time. For example, for a sinusoidal wave having frequency xcfx89, Ex=A sin(xcfx89t) and Ey=B sin((xcfx89t)+xcex1), where xcex1 is time, a is a phase difference and A and B are the magnitudes of the Ex and Ey components. When the Ex and Ey components are in phase (xcex1=0), the electric field is linearly polarized. In this condition, the electric field vector at a given point always lies on the same plane. When the Ex and Ey components are out of phase (xcex1xe2x89xa00), elliptical polarization results. When the Ex and Ey components of an elliptically polarized electromagnetic signal are of equal magnitude (A=B) and are 90xc2x0 or 270xc2x0 out of phase, the signal is said to be circularly polarized.
To measure signal polarization, a dual-aperture (polarized) antenna and a device known as a polarimeter are required. The dual-aperture antenna provides one electrical signal Vh representing the Ex or horizontal component of the electric field of a signal impinging on the antenna, and another electrical signal Vv representing the Ey or vertical component of the electric field of the same signal. These signals typically are amplified and filtered separately in a dual-channel receiver before passing to the polarimeter. The polarimeter compares these signals to determine their relative magnitudes and the phase difference between them.
A prior art analog polarimeter is shown in FIG. 1. The horizontal signal Vh is supplied to one input of a four port directional coupler 200 of a type referred to as a xe2x80x9chybrid.xe2x80x9d The vertical signal Vv is supplied to the input of a phase shifter 202 which applies a known phase shift xcfx86 to that signal. The phase-shifted signal is supplied to another input of the directional coupler 200. The coupler 200 provides a signal at a first output 204 representing the coupled power output or sum of the input signals supplied to the circuit, and also provides a signal representing a specific phase shift between the input signals at a second output 206. In this prior art example, the phase shift is 180xc2x0. The first or sum output 204 of circuit 200 is supplied to the input of a further phase shifter 208 which applies a known phase shift. The output of this phase shifter is connected to one input of another directional coupler 210, which is similar to the first 200. The second or difference output 206 of combining circuit 200 is connected directly to the other input of combining circuit 210. Thus, when time-varying Vv and Vh signals are applied to the polarimeter, one time-varying output signal, referred to as the xcex94 signal appears at the difference output 212 of coupler 210. Another time-varying output signal referred to as the xcexa3 signal, appears at the sum output 214 of coupler 210. The output signals are supplied to a dual channel receiver and logarithmic amplifier 216 which monitors the amplitudes of these signals and provides a signal representing a ratio between their amplitudes. This ratio signal is supplied to a null adaptive tracker 218, which adjusts the phase differences xcfx86 and applied by the phase shifters to achieve a null condition as discussed below.
The relationships between the xcex94 and xcexa3 output signals appearing at outputs 212 and 214 and the input signals Vv and Vh are referred to as the xe2x80x9ctransfer functionsxe2x80x9d of the polarimeter. These transfer functions depend on the phase shifts xcfx86 and xcex3 applied by phase shifters 202 and 208. Conversely, there is a relationship between the transfer functions which yield output signals with particular characteristics and the phases and amplitudes of Vv and Vh. Stated another way, there is a relationship between the phase shifts xcfx86 and xcex3 which yield particular output signal characteristics and the phases and amplitudes of the input signals Vv and Vh.
In particular, for the components illustrated in FIG. 1, the ratio       "LeftBracketingBar"    Δ    "RightBracketingBar"        "LeftBracketingBar"    Σ    "RightBracketingBar"  
between the amplitude |xcex94| of the xcex94 output signal and the amplitude |xcexa3| of the xcexa3 output signal will be at a minimum or null condition when:                               γ          =                      2            ⁢                          xe2x80x83                        ⁢                          tan                              -                1                                      ⁢                          xe2x80x83                        ⁢                          (                              b                a                            )                                      ,        and                            (        1        )                                φ        =                                            3              ⁢                              xe2x80x83                            ⁢              π                        2                    -                      α            .                                              (        2        )            
Where:
a is the amplitude of the horizontal component Vh;
b is the amplitude of the vertical component Vv; and
xcex1 is the phase difference between these components.
Solving for the amplitude ratio   b  a
and phase difference xcex1 from the xcex3 and values,                                           b            a                    =                      tan            ⁢                          xe2x80x83                        ⁢                          (                              γ                2                            )                                      ,        and                            (        3        )                                α        =                  φ          -                                                    3                ⁢                                  xe2x80x83                                ⁢                π                            2                        .                                              (        4        )            
Thus, the parameters which characterize the polarization of the signal, such as the amplitude ratio   b  a
and phase difference xcex1 between the components of the signal can be found from the phase shifts xcfx86 and xcex3 which yield the null condition or minimum ratio             "LeftBracketingBar"      Δ      "RightBracketingBar"              "LeftBracketingBar"      Σ      "RightBracketingBar"        .
Tilt angle, xcfx84, of an elliptically polarized signal is also derivable from the polarimeter phase shift angles xcex3 and xcfx86 at the null condition as                     τ        =                              1            2                    ⁢                      xe2x80x83                    ⁢                                                    tan                                  -                  1                                            ⁡                              [                                  tan                  ⁢                                      xe2x80x83                                    ⁢                                      (                                          2                      ⁢                                              xe2x80x83                                            ⁢                      γ                                        )                                    ⁢                                      xe2x80x83                                    ⁢                  cos                  ⁢                                      xe2x80x83                                    ⁢                                      (                                          φ                      -                                                                        3                          ⁢                                                      xe2x80x83                                                    ⁢                          π                                                2                                                              )                                                  ]                                      .                                              (        5        )            
In operation, tracker 218 sets phase shifter 208 to hold xcex3 constant at an arbitrary value and adjusts phase shifter 202 to vary xcfx86 in an iterative or trial-and-error process until the output ratio       "LeftBracketingBar"    Δ    "RightBracketingBar"        "LeftBracketingBar"    Σ    "RightBracketingBar"  
is at a minimum for the arbitrary value of xcex3. The tracker 218 then holds xcfx86 constant and adjusts phase shifter 208 to vary xcex3 in a further iterative process until the true minimum or null condition is found.
Other known analog polarimeters use different networks, typically including phase shifters and mixers. However, the overall principle of operation is the same. The transfer function or functions of the polarimeter is adjusted iteratively to yield output signals having predetermined characteristics, and the polarization of the signal is found from the transfer function or functions which yield those characteristics. Polarimeters of this type can provide accurate measurements of signal polarization. However, they require considerable time to perform the required iterations.
One aspect of the present invention provides apparatus for determining the polarization of a signal having vertical and horizontal components. Apparatus according to this aspect of the invention includes a first register for storing a first series of discrete values representing a series of samples of the horizontal component and a second register for storing a second series of discrete values representing a series of samples of the vertical component. The different values in each series can be denoted by an integer index. For example, a series of N horizontal sample values can be represented as A(1),A(2) . . . A(N) or, generically, A( ) where the parenthetical expression represents the index, and the vertical samples values can be represented by B( ).
The apparatus also includes a plurality of sets of calculation elements which are arranged to combine values in the first and second series with one another so as to produce one or more output values. Typically, the calculation elements are arranged to operate cyclically, so that a reference value in one series of sample values is combined with other values in the other series, in the same series, or both during each cycle of such set, to yield one or more output values for each cycle. Operation of each set of calculation elements through numerous cycles, using different values in one series of input values as the reference value, yields one or more series of output values. Each set of calculation elements has one or more transfer functions specifying the manner in which different samples in the series are combined with one another. These transfer functions typically include one or more integer offsets specifying the differences between the index of the reference value used on a particular cycle and the index of each other value to be combined with the reference value on that cycle. Preferably, the transfer functions used by different sets of calculation elements are different from one another. At least some of these different sets of calculation elements are arranged to operate in parallel with one another.
The apparatus also includes an evaluation circuit connected to the various sets of computation elements. The evaluation circuit is arranged to compare one or more characteristics of the series of output values generated by the various sets of calculation elements with one or more preselected characteristics, and to select the series having characteristics corresponding to preselected characteristics. This selection inherently identifies the set of computation elements which provided such series, and thus identifies the offsets used in the transfer function of that set. The identified offsets provide information about the polarization of the signal.
Operation of an individual set of calculation elements, with particular offsets, is analogous to operation of an analog polarimeter with particular phase delays. However, because numerous sets of calculation elements operate in parallel with one another, the need for iteration is reduced or eliminated. Only a small number of cycles are required to determine signal polarization. Polarization measurement can be accomplished rapidly, even where many different offsets are used to provide a fine phase resolution as required for a high-accuracy polarization measurement, and even where each series of sample values includes thousands of sample values.
For example, a polarimeter according to one embodiment of the present invention includes numerous sets of calculation elements in the form of adders connected to the registers to provide transfer functions of the form:
xcex1(k,i,j)=A (k)xe2x88x92B(k+i)xe2x88x92[A(k+j)+B(k+i+j)], (6)
xcexa3(k,i,j)=A (k)xe2x88x92B(k+i)+[A(k+j)+B(k+i+j)], (7)
In these functions, k is the index of the reference sample A(k) whereas i and j are the offsets and xcex94( ) and xcexa3( ) are two series of output values produced by each set of calculation elements. These particular transfer functions are analogous to the transfer functions of the analog polarimeter discussed above. For series of input sample values A( ) and B( ) corresponding to particular input signals Vv and Vh, a set of these transfer functions with particular offsets i and j will provide series of output values xcex94( ) and xcexa3( ) corresponding to the xcex94 and xcexa3 output signals of the analog polarimeter of FIG. 1 using particular phase shifts xcfx86 and xcex3. Differences in j and i have effects analogous to differences in xcfx86 and xcex3, respectively. However, because the various sets of calculation elements operate in parallel with one another, it is unnecessary to vary each phase shift iteratively.
For example, in an ideal polarimeter according to this embodiment of the invention, a first group of N sets of calculation elements having transfer functions with different values of j but with the same value of i are operated in parallel, and the series of output values which yields the lowest amplitude ratio       "LeftBracketingBar"    Δ    "RightBracketingBar"        "LeftBracketingBar"    Σ    "RightBracketingBar"  
is selected to thereby select a value of j.
That selected value of j is used in operation of a second group of M sets of calculation elements each having transfer functions with the selected value of j but with different values of i. Here again, the series of output values which yields the lowest value of       "LeftBracketingBar"    Δ    "RightBracketingBar"        "LeftBracketingBar"    Σ    "RightBracketingBar"  
is selected, which in this case results in selection of a value i. The selected values of i and j can be converted into the polarization parameters of the signal, such as the as the amplitude ratio   b  a
between the vertical and horizontal components , the phase difference xcex1 and the tilt angle xcfx84. Where each series of input sample values A( ) and B( ) includes K samples, the polarization of the signal can be determined in slightly more than 2K clock cycles.
Most preferably, each set of calculation elements is associated with one or more characteristic-calculation circuits, and the characteristic-calculation circuit associated with each set of calculation elements operates in parallel with the calculation elements of that set, and in parallel with the characteristic-calculation circuits associated with other sets. For example, where the characteristics of the output series which are examined include amplitude, the characteristic-calculation circuits associated with each set of calculation elements may include one or more accumulators each arranged to add an output value calculated on each cycle of the calculation elements to a total. For example, where each set of calculation elements provides a xcex94( ) value and a xcexa3( ) output value on each cycle, the characteristic-calculation circuits associated with each set may include one accumulator for adding the xcex94( ) value produced on each cycle to a total xcexa3( ) and another accumulator for adding the xcexa3( ) value produced on each cycle to a total xcexa3xcexa3. Essentially, no additional time is required to calculate the amplitudes of the output signals from the various sets of calculation elements.
In a particularly preferred arrangement, the registers used to hold the series of input sample values include shift registers. The different offsets used in the transfer functions of the various sets of calculation elements are established by connecting the different calculation elements to different taps of the shift registers. The reference value used in each cycle of the calculation elements is changed by clocking the data through the shift registers.
A further aspect of the present invention provides methods of determining the polarization of a signal from a series of horizontal input sample values and a series of vertical input sample values. Methods according to this aspect of the invention desirably start with a calculating a plurality of series of output values, using a plurality of sets of transfer functions. Most preferably, calculations using at least some of the sets of transfer functions are conducted in parallel with other calculations using other transfer functions. As discussed above in connection with the apparatus, the transfer functions represent combination of samples in the two series with a reference sample value. Each transfer function includes one or more integer offsets specifying the differences between the index of the reference value used on a particular cycle and the index of each other value to be combined with the reference value on that cycle. The transfer functions in different sets desirably include different offsets. The method desirably further includes the step of evaluating one or more characteristics of the series of output values computed using the transfer functions of the different sets according to a predetermined criterion, and selecting the series produced by one sets of calculations based on such evaluation. As discussed above in connection with the apparatus, this selection implicitly selects one set of calculations and thus selects one set of offsets, from which the polarization characteristics of the signal can be determined calculation of numerous series of output values in parallel with one another minimizes the need for iteration.
Particularly preferred methods according to this aspect of the invention, one or more characteristics of each series of output values are calculated in parallel with calculation of the output values themselves. Methods according to this aspect of the invention can provide rapid polarization measurements.
Other objects and advantages of the system and method will become apparent to those skilled in the art after reading the detailed description of the preferred embodiment.